Distorted-wave Born Approximation Analysis Research Articles

Transfer reactions for 28Si

Cross sections of one- and few-nucleon transfers in the reaction /sup 28/Si+ /sup 28/Si at E/sub lab/ -- 151.25 MeV have been measured with a quadrupole-dipole-dipole-dipole magnetic spectrometer. The one-neutron and one-proton transfers to corresponding shell model states in the pairs of mirror nuclei /sup 29/Si-/sup 29/P and /sup 27/Si-/sup 27/Al are found to be approximately equal. The cross sections for few-nucleon transfers to states with excitation energies E/sub x/<5 MeV exhibit a strong enhancement of 1n1p over 2n and 2p and of 2n2p (i.e., 1..cap alpha..) over 2n1p or 1n2p transfers. A distorted-wave Born approximation analysis of the 1n and 1p transfers was performed. The derived spectroscopic factors display a high degree of symmetry with respect to isospin and are consistent with the widely varying values obtained in light ion studies.

36,38Ar(d-bar, alpha )34,36Cl reactions induced by tensor polarized deuterons.

Exact finite-range distorted-wave Born approximation analyses of cross section and vector and tensor analyzing power angular distributions for some /sup 36,38/Ar(d-arrow-right,..cap alpha..) transitions induced by 16 MeV polarized deuterons have been performed using full s-italicd-italic-shell model wave functions and including a D-italic-state amplitude for the ..cap alpha.. particle. The L-italic-mixing ratios R-italic for several unnatural parity transitions have been determined from comparisons of the calculations with the tensor analyzing power data. Shell-model calculations are found to be in agreement with the experimentally obtained phases of R-italic, while the predicted magnitudes agree well in some cases.

Effects of nuclear correlations on low-energy pion charge-exchange scattering.

An isospin-invariant optical-potential framework is used to make a coordinated analysis of low-energy pion elastic and single- and double-charge-exchange scattering to isobaric analog states. The form of the potential studied here is motivated by the work of Stricker, McManus, and Carr, who emphasized the importance of isoscalar absorption-dispersive and correlation effects for low-energy pion elastic scattering. In this paper we examine the influence of the corresponding isovector and isotensor nuclear correlations on low-energy charge exchange. Comparison of our results to 50 MeV data supports the existence of the isovector correlation terms, but shows a need for an additional isotensor effect. A distorted-wave Born approximation analysis confirms that distortions are weak (the mean density of interaction is roughly 50% of the central value), but demonstrates that distortions of the pion waves by the nuclear medium cannot be neglected in describing charge exchange.

Inelastic proton excitation of high-lying giant resonances.

Inelastic scattering of 800 MeV protons has been studied for targets of $^{208}\mathrm{Pb}$, $^{144}\mathrm{Sm}$, and $^{116}\mathrm{Sn}$. At excitation energies above particle emission threshold a spectrum of giant resonances is clearly in evidence. Angular distributions were extracted for the high-lying peaks (\ensuremath{\sim}20 MeV excitation energy) in $^{208}\mathrm{Pb}$ and $^{144}\mathrm{Sm}$. Collective model distorted-wave Born approximation analyses of these data show that isoscalar octupole and dipole states dominate the spectra.

Quasi-elastic processes in the 28Si+40Ca reaction at 225 MeV.

Elastic, inelastic, and single-nucleon transfer data are reported for $^{28}$Si${+\mathrm{}}^{40}$Ca at ${E}_{\mathrm{lab}=225}$ MeV. Standard optical model and distorted-wave Born approximation analyses of the elastic and inelastic scattering angular distributions have been performed resulting in good descriptions of the data. In the inelastic scattering analysis, the nuclear deformation lengths were found to be consistent with the Coulomb deformation lengths obtained from electron scattering. The data for one-nucleon transfers were analyzed using the distorted-wave Born approximation with the optical potential fitted to the elastic scattering and the spectroscopic factors taken from light-ion studies. With the exception of small shifts in angle, the distorted-wave Born approximation correctly predicts the shapes of the angular distributions and the relative intensities of transitions to different states populated in the same reaction. The magnitudes of the single-particle transfer cross sections are reproduced to within a factor of 1.5. However, the distorted-wave Born approximation fails to predict the nearly 40% difference in the magnitudes of the cross sections observed for the ${(}^{28}$Si, $^{27}\mathrm{Si}$) and ${(}^{28}$Si, $^{27}\mathrm{Al}$) reactions, which populate mirror states.

Multinucleon transfer reactions with 7Li

The three-, four-, and five-nucleon transfers were investigated by studying the $^{10}\mathrm{B}$(\ensuremath{\alpha},${\mathrm{}}^{7}$Li${)}^{7}$Be, $^{11}\mathrm{B}$${(}^{3}$He${,}^{7}$Li${)}^{7}$Be, and $^{12}\mathrm{C}$(d${,}^{7}$Li${)}^{7}$Be reactions, respectively. The measurements were performed in the entire center of mass angular region, at incident energies corresponding to 49.3 MeV in the center of mass system of the exit channel. A distorted-wave Born approximation analysis was performed including second-order transfer contributions for all investigated reactions.

Proton stripping to outer subshells and the damping of single-particle states: 116Sn, 144Sm, and 208Pb( alpha,t) reactions at 80 MeV.

The stripping reaction (\ensuremath{\alpha},t) at 80 MeV incident energy has been used to study the proton-particle response function on $^{116}\mathrm{Sn}$, $^{144}\mathrm{Sm}$, and $^{208}\mathrm{Pb}$ target nuclei up to 22 MeV excitation energy. Rather complete spectroscopic information has been obtained on the low-lying proton states (0--3 MeV) through angular distribution measurements and standard distorted wave Born approximation analysis. Strong transitions to high-lying proton states located between 5 and 12 MeV excitation energy in $^{145}\mathrm{Eu}$ and $^{209}\mathrm{Bi}$ are observed whereas the spectrum from the $^{116}(\mathit{\ensuremath{\alpha}}$,t) reaction displays only broad, weak enhancement of cross sections at high excitation. These transitions appear as broad bumps superimposed on a continuous background for which a qualitative analysis within the framework of the breakup model has been attempted. The excitation energies, angular distributions, and strengths of these high-lying transitions suggest that they arise from proton stripping to high-spin outer subshells, e.g., 1h(9/2) and 1i(13/2) in $^{145}\mathrm{Eu}$, and 1i(11/2) and 1j(15/2) in $^{209}\mathrm{Bi}$. A distorted-wave Born approximation analysis using resonant form factors for the states located above the proton threshold has been carried out. The deduced proton strength distributions are compared with the predictions from the quasiparticle-phonon and single-particle vibration coupling nuclear models. Around 12--14 MeV excitation energy, narrow peaks corresponding to the population of the isobaric analog states in $^{117}\mathrm{Sb}$ and $^{145}\mathrm{Eu}$ are also observed. Our results are compared to the known spectroscopic properties of the corresponding parent states in $^{117}\mathrm{Sn}$ and $^{145}\mathrm{Sm}$.

Microscopic and semimicroscopic analysis of the reaction 27Al(p, alpha )24Mg in the energy range between 20 and 45 MeV.

The microscopic model of the distorted-wave Born approximation theory for (p,\ensuremath{\alpha}) reactions formulated in the isospin representation is compared with a semimicroscopic analysis using cluster form factors and SU(3) spectroscopic amplitudes. The differential cross sections of \ensuremath{\alpha} particles emitted in the reaction $^{27}\mathrm{Al}$(p,\ensuremath{\alpha}${)}^{24}$Mg have been measured at the bombarding energies 20, 24, 30.5, and 45 MeV. The microscopic as well as the semimicroscopic distorted-wave Born approximation analysis reproduces the angular distributions in a large range of incident energies when using energy-dependent optical potentials. The relative intensities of the transitions to the ground state and excited states up to ${E}_{x}$=6 MeV are described quite well in the semimicroscopic analysis.

α-ParticleD-State Components from (d,α) Analyzing Powers

A D-state component in the ..cap alpha.. particle has been extracted from angular distributions of tensor analyzing powers for /sup 89/T(d,..cap alpha../sub 0/) /sup 87/Sr at 9, 12, and 16 MeV. Exact finite-range distorted-wave Born approximation analyses including the effects of L and J mixing have been performed. The D-state parameter D/sub 2/, closely related to the asymptotic D- to S-state ratio for d-d relative motion in the ..cap alpha.. particle, requires a value of D/sub 2/ = -0.3 +- 0.1 fm/sup 2/ in order to fit the tensor analyzing power data.

Excitation of the ground state rotational band inNe20by 0.8 GeV protons

Angular distributions for the scattering of 0.8 GeV polarized protons from the ground state rotational band in $^{20}\mathrm{Ne}$ are reported. Cross sections and analyzing powers for protons exciting these states were measured with a high resolution spectrometer. Coupled channels and distorted wave Born approximation analyses of scattering data for the ${0}^{+}$, ${2}^{+}$, ${4}^{+}$, and experimentally unresolved ${6}^{+}$ states are presented. The observed cross section data for the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states are reproduced quite well with the coupled channels calculations, and the large hexadecapole deformation reported previously is confirmed. The distorted wave Born approximation results are equally good for the ${0}^{+}$ angular distribution, but are a significantly poorer representation of the cross section data for the ${2}^{+}$ and ${4}^{+}$ states. Both calculations do equally well in explaining the ${0}^{+}$ analyzing power data and both fail to explain the ${4}^{+}$ analyzing power data past the region of the first maximum. The coupled channels results do a better job in explaining the ${2}^{+}$ analyzing power data. The multipole moments of the deformed optical potential used in the coupled channels calculations are related to those of the matter distributions by Satchler's theorem. These are compared to the moments found using other hadronic probes, those of the charge distribution determined by electromagnetic measurements, and to moments from shell model and Hartree-Fock calculations.

Energy dependence of neutron scattering fromPb208in the energy range 7—50 MeV

Elastic neutron scattering from $^{208}\mathrm{Pb}$ has been measured at 22.0 and 24.0 MeV and remeasured at 7.0 and 20.0 MeV with greatly improved precision. The present results and other neutron data in the energy range 7---50 MeV are analyzed in terms of a conventional, local optical model potential with the aim of studying energy dependence of the potential well depths. We find that the very detailed measurements of the present work made unusual demands on the geometrical parameters of the model. Improvements, if any, resulting from extension of the optical model parametrization to include a real surface term and imaginary spin-orbit term are tested. Concurrently with the elastic scattering experiments, inelastic scattering to the ${3}^{\ensuremath{-}}$ state at 2.615 MeV was measured at 7.0, 20.0, and 22.0 MeV. A distorted-wave Born approximation analysis is made of these data to extract octupole deformation parameters.

Levels inK38from theCa40(d, α)reaction at 22.8 MeV

Twenty levels in $^{38}\mathrm{K}$ up to an excitation energy of 10.26 MeV have been identified in a study of the $^{40}\mathrm{Ca}(d, \ensuremath{\alpha})^{38}\mathrm{K}$ reaction at an incident deuteron energy of 22.8 MeV. Differential cross sections were measured at forty-four angles in an angular range $11\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}165\ifmmode^\circ\else\textdegree\fi{}$. Distorted-wave Born approximation analysis has been performed for eight transitions using two-nucleon spectroscopic amplitudes derived from a full $\mathrm{sd}$ shell-model calculation. For other levels, distorted-wave Born approximation calculations were performed assuming simple two-nucleon configurations. The 7.32-MeV level is found to be populated by $L=0+2$ transfer and hence has ${J}^{\ensuremath{\pi}}={1}^{+}$. A newly identified level at 9.88 MeV is found to be excited by $L=2$ transfer and hence has ${J}^{\ensuremath{\pi}}={1}^{+}, {2}^{+}, or {3}^{+}$.NUCLEAR REACTIONS $^{40}\mathrm{Ca}(d, \ensuremath{\alpha})^{38}\mathrm{K}$, ${E}_{d}=22.8$ MeV, measured ${E}_{\ensuremath{\alpha}}$ and $\ensuremath{\sigma}(\ensuremath{\theta}, {E}_{\ensuremath{\alpha}})$, DWBA analysis, deduced levels, $L$ transfer.

Giant resonance excitation in theAl27(Li6,He6)Si27reaction at 93 MeV

A giant resonance in /sup 27/Si is observed in the excitation energy region of 10--18 MeV in the spin-isospin flip /sup 27/Al(/sup 6/Li, /sup 6/He)/sup 27/Si reaction. A microscopic distorted-wave Born approximation analysis using a G-matrix nucleon-nucleon force and a local energy approximation knockout exchange correction indicates multipolarities between lambda = 3 and lambda = 5 for the giant resonance.

Cluster representation ofLi6and the finite-range distorted-wave Born approximation analysis ofLi6-induced alpha transfer reactions

With a view to examine the suitability of the various different forms of $\ensuremath{\alpha}\ensuremath{-}d$ cluster representation of $^{6}\mathrm{Li}$ used in the literature based on different criteria for the $\ensuremath{\alpha}$-transfer reaction analysis, finite-range distorted-wave Born approximation calculations have been made in the present work for ($^{6}\mathrm{Li}$,$d$) reactions with various forms of cluster representation of $^{6}\mathrm{Li}$ and they are compared with the angular distribution data on the targets $^{26}\mathrm{Mg}$, $^{27}\mathrm{Al}$, $^{29}\mathrm{Si}$, and $^{31}\mathrm{P}$ at a bombarding energy of 36 MeV. It is found that (a) the single node wave function ${\ensuremath{\psi}}_{\ensuremath{\alpha}d}$ introduced by Kubo and Hirata with the corresponding Woods-Saxon form of ${V}_{\ensuremath{\alpha}d}$ is not found to fit the angular distribution data at all, (b) the zero node Eckart function form of ${\ensuremath{\psi}}_{\ensuremath{\alpha}d}$ with the corresponding ${V}_{\ensuremath{\alpha}d}$ with attractive and repulsive parts is also not successful, and (c) the zero node wave function generated by a Woods-Saxon form of a potential with a hard repulsive core of ${R}_{\mathrm{core}}=1.25$ fm introduced by Watson et al. is also unsatisfactory. However, the Watson form modified by reducing the hard core radius to ${R}_{\mathrm{core}}=0.6$ fm predicts angular distributions satisfactorily. These results are not affected by the different choices of optical model parameters.NUCLEAR REACTIONS ($^{6}\mathrm{Li}$,$d$), FRDWBA calculations with different $\ensuremath{\alpha}\ensuremath{-}d$ cluster representations of $^{6}\mathrm{Li}$. Compared $\ensuremath{\sigma}(\ensuremath{\theta})$ data.

"Stretched"6−T=1State inAl24Observed in the ReactionMg24(p, n)Al24

An isovector $M6$ transition is observed for the first time in a ($p, n$) reaction. A prominent peak was seen at ${E}_{x}=5.545\ifmmode\pm\else\textpm\fi{}0.025$ MeV in $^{24}\mathrm{Al}$ in the study of the reaction $^{24}\mathrm{Mg}(p, n)^{24}\mathrm{Al}$ at ${E}_{p}=35$ MeV. This state is interpreted as the "stretched" particle-hole state with ${J}^{\ensuremath{\pi}}={6}^{\ensuremath{-}}$, $T=1$, which corresponds to the 15.13-MeV state in $^{24}\mathrm{Mg}$. Distorted-wave Born approximation analysis gives a result consistent with those for ($p, {p}^{\ensuremath{'}}$) and ($e, {e}^{\ensuremath{'}}$) reactions, indicating that at least 50% of the isovector $M6$ strength is missing.

Elastic and inelastic scattering of 0.8 GeV protons fromMg24andMg26

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$ are presented. Cross sections for protons exciting states of energy up to about 10 MeV are measured using a high resolution spectrometer. Coupled channels analyses of scattering data to the ${0}^{+}$, ${2}^{+}$, ${4}^{+}$, and ${6}^{+}$ states in the ground state rotational band, the ${2}^{+}$, ${3}^{+}$, ${4}^{+}$, and ${6}^{+}$ states in the $\ensuremath{\gamma}$-vibrational band, the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states in the $\ensuremath{\beta}$-vibrational band, and the ${3}^{\ensuremath{-}}$ and ${5}^{\ensuremath{-}}$ members of the ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}} \mathrm{and} {3}^{\ensuremath{-}}$ vibrational bands in $^{24}\mathrm{Mg}$ are presented. Also reported are coupled channels analyses of the experimental angular distributions in $^{26}\mathrm{Mg}$ for the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states in the ground state band, the possible ${2}^{+}$, ${3}^{+}$, and ${4}^{+}$, $\ensuremath{\gamma}$-band members, and several ${3}^{\ensuremath{-}}$ members of ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}} \mathrm{and} {3}^{\ensuremath{-}}$ bands. The data for the ${3}^{\ensuremath{-}}$ states in both $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$ differ both in shape and angular positions of the maxima and minima. Coupled channels analyses are able to account for these differences in the ${3}^{\ensuremath{-}}$ experimental cross sections by selecting ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}} or {3}^{\ensuremath{-}}$. This is believed to be the first observation of "$K$ dependence" for $l=3$ excitations in inelastic scattering by $s\ensuremath{-}d$ shell nuclei. Distorted wave Born approximation analyses of the other states in $^{26}\mathrm{Mg}$ excited by $l$ transfers from 2 to 4 are also described. Several new assignments of ${J}^{\ensuremath{\pi}}$ for excited states in $^{26}\mathrm{Mg}$ are proposed based upon the distinctive $l$ transfer dependence found in the positions of the first maximum and in the general shapes of the angular distributions. Multipole moments extracted from the deformed optical potentials are related to those of the matter distributions by Satchler's theorem. These are compared to multipole moments obtained from analyses of hadronic scattering data, as well as with the moments of the charge distributions determined by electromagnetic measurements.NUCLEAR REACTIONS $^{24,26}\mathrm{Mg}$($p$,${p}^{\ensuremath{'}}$), $E=0.8$ GeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, enriched targets; resolution \ensuremath{\ge}80 keV, ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=5.49\ifmmode^\circ\else\textdegree\fi{} \mathrm{to} 31.66\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=0.1\ifmmode^\circ\else\textdegree\fi{}$. Optical model potential, DWBA analysis, coupled channels analysis, symmetric and asymmetric rotational model, coupling parameters, multipole moments, assigned ${J}^{\ensuremath{\pi}}$.

Excited states ofTc102: A study of the proton-neutron interaction

Levels in $^{102}\mathrm{Tc}$ up to an excitation energy of 1 MeV were studied by means of the $^{100}\mathrm{Mo}$($^{3}\mathrm{He}$,$p$)$^{102}\mathrm{Tc}$ and $^{104}\mathrm{Ru}$($d$,$\ensuremath{\alpha}$)$^{102}\mathrm{Tc}$ reactions at incident energies of 25 and 20 MeV, respectively. Tentative spin assignments were deduced from distorted-wave Born approximation analyses of the proton angular distributions. The results are discussed in the framework of the shell model.NUCLEAR REACTIONS $^{100}\mathrm{Mo}$($^{3}\mathrm{He}$,$p$), ${E}_{^{3}\mathrm{He}}=25$ MeV; measured $\ensuremath{\sigma}({E}_{p},\ensuremath{\theta})$, $\ensuremath{\theta}=5\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}40\ifmmode^\circ\else\textdegree\fi{}$. $^{104}\mathrm{Ru}$($d$,$\ensuremath{\alpha}$), ${E}_{d}=20$ MeV; measured ${E}_{\ensuremath{\alpha}}$ at $\ensuremath{\theta}=15\ifmmode^\circ\else\textdegree\fi{}$. Enriched targets. Split-pole spectrograph. $^{102}\mathrm{Tc}$ deduced levels, tentative ${L}_{\mathrm{np}}$,${J}^{\ensuremath{\pi}}$. DWBA analysis. Calculated: $\ensuremath{\pi}1{g}_{\frac{9}{2}}\ensuremath{\nu}1{g}_{\frac{7}{2}}$ proton-neutron multiplet structure.

2.217 MeV state inAr37

Cross section and vector analyzing power data for the 2.217 MeV state in $^{37}\mathrm{Ar}$ have been measured via the ($d,p$) reaction at an incident deuteron energy of 11 MeV. Distorted wave Born approximation analysis of the data establishes the spin parity of this relatively weak state as 7/${2}^{+}$. The data are fairly well reproduced by the calculations indicating that the one-step process plays a dominant role in populating the state in the ($d,p$) reaction. The spectroscopic factor for the state is found to be 0.04\ifmmode\pm\else\textpm\fi{}0.01. Model calculations indicate that two-step and compound nuclear processes have negligible effects on the conclusions.[NUCLEAR REACTIONS $^{36}\mathrm{Ar}(\stackrel{\ensuremath{\rightarrow}}{d},p)$, $E=11.0$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$, $i{T}_{11}(\ensuremath{\theta})$. Deduced $J$, $\ensuremath{\pi}$, $S$. DWBA analysis.]

Li6real potential volume integrals in elastic scattering and distorted-wave Born approximation analyses

The magnitudes of volume integrals per interacting nucleon pair ${J}_{R}$ calculated from a compilation of $^{6}\mathrm{Li}$ potentials vary between 100 and 500 MeV ${\mathrm{fm}}^{3}$. They are grouped in discrete branches with ${J}_{R}(A)$ smoothly increasing with decreasing target mass. Comparison with the results for lighter projectiles restricts the "physically meaningful" branches to those characterized by ${J}_{R}(A\ensuremath{\ge}48)\ensuremath{\le}270$ MeV ${\mathrm{fm}}^{3}$. ($^{6}\mathrm{Li},d$) reaction analyses yield the same fit qualities for $^{6}\mathrm{Li}$ potentials of the different discrete families, but deduced spectroscopic factors jump (by factors of \ensuremath{\sim}3) when changing between successive families.NUCLEAR REACTIONS $^{6}\mathrm{Li}$ optical potential volume integrals compared with volume integrals for lighter projectiles, discussed discrete ambiguities in ($^{6}\mathrm{Li},d$) DWBA; target masses $A=16 \mathrm{to} 64$, $E(^{6}\mathrm{Li})=30$ MeV.

Zero-range distorted-wave Born approximation analysis of (p,t) transfer reactions

Zero-range distorted-wave Born approximation calculations are used to investigate the systematics of two-nucleon transfer reactions. The shapes of the calculated 40Ca(t,p)42Ca(gs) and 208Pb(p,t)206Pb(gs) cross sections are relatively insensitive to details of the core plus two-neutron form factor, if the form factor tails have similar shapes. Studies of heavy targets such as 206Pb suggest a surface reaction mechanism, but lighter targets (16O and 40Ca) indicate that spatial regions beyond the target surface provide the dominant contribution to the (p,t) cross section.